Note: We might also have expressed the critical value as a z score. Because the sample size is fairly large, a z score analysis produces a similar result-a critical value equal to 2.58. 1  Compute margin of error (ME): ME = critical value * standard error = 2.61 * 0.82 = 2.1. 2  Specify the confidence interval.3  margin of error.he Variability of the Sample Mean. To construct a confidence interval for a sample mean, we need to know the variability of the sample mean. This means we need to know how to compute the standard deviation or the standard error of the sampling distribution.
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